REM WORKING PAPER SERIES
Endogenous Quality and Firm Entry
Rui Faustino
REM Working Paper 0107-2019
December 2019
REM – Research in Economics and Mathematics Rua Miguel Lúpi 20,
1249-078 Lisboa, Portugal
ISSN 2184-108X
Any opinions expressed are those of the authors and not those of REM. Short, up to two paragraphs can be cited provided that full credit is given to the authors.
Endogenous Quality and Firm Entry∗
Rui Faustino†
Update: November, 2019
Abstract
During economic expansions the net product creation and average product quality increase as firms in-
troduce new products with higher quality. The introduction of new products with higher quality produces
a quality bias in price level measures. In this paper I develop a firm-entry model with endogenous quality
of consumer goods. Following a TFP shock, the price level increases not only due to a larger number of
varieties but also due to a higher average quality. Simultaneously, the channel of endogenous quality acts
as a propagation mechanism to other variables in the economy, amplifying their response to shocks. This
channel can also be either contractionary or shut down, depending on how consumers derive utility from
quality.
Keywords: Firm-entry, business cycle, quality, prices.
JEL codes: E32, E20, L11
1 Introduction
Empirical evidence suggests that net product creation is linked to improvements in the quality of goods
and heavily procyclical, as replacement of outdated goods by new ones is accelerated during booms - Broda
and Weinstein (2010). Furthermore, net product creation is mainly determined by firm entry rather than
firm exit. Simultaneously, an extensive literature has been produced on general equilibrium models with
endogenous firm entry1, capable of explaining the dynamics of product creation. However, these models do
not account for the dynamics in quality and its role as propagation mechanism to the rest of economy, mainly
markups and prices2.∗I would like to thank to Luís Costa, the participants of 13th Lisbon Macro Club for the useful comments and suggestions.†ISEG - School of Economics & Management, Universidade de Lisboa; UECE – Research Unit on Complexity and Economics.
Email: [email protected] and Floetotto (2008), Colciago and Etro (2010) and Bilbiie et al. (2012) are the main examples of these type of
models.2Two exceptions are the models in Schmitt-Grohé and Uribe (2012) and Jaimovich et al. (2019). Schmitt-Grohé and Uribe
(2012) develop a model with exogenously-determined quality and analyze the importance of quality bias in the setting of inflationtargets. Jaimovich et al. (2019) study the trading down in consumption during recessions using a general equilibrium model withendogenous quality.
1
In this study, I address this shortcoming by introducing endogenous quality into an otherwise standard
endogenous firm-entry model. Following a productivity shock, the model generates a positive response of
firm creation and average quality level, leading to an increase in the price level. This is consistent, not only
with the empirical evidence for net product creation, but also with the findings in Bils (2009) and Broda and
Weinstein (2010) of the role of quality improvements in price level dynamics.
In these studies, the authors find that quality improvements account for a significant part of inflation and
since statistical authorities do not adjust fully the impact of quality in prices, the inflation rate is consistently
overestimated (i.e. quality bias). Likewise as price level is partially determined by quality in the model, the
changes in the unadjusted price level are significantly higher than when one accounts for the quality bias.
Since the framework is the standard firm-entry model, the model with endogenous quality maintains its
features, such as the procyclical behavior of firm entry and countercyclical response of markups. However,
with endogenous quality the model adds one more propagation channel to productivity shocks and the
response of the main variables is amplified. Prices and markups, as well as consumption and output, are
now determined by the interaction between the number of firms (varieties) and average quality level.
The effect on other variables crucially depends on marginal utility of quality to consumers. When the
marginal utility is constant, the channel of transmission of changes in quality to the rest of the economy is
broken and the model produces the same results as in Hamano and Zanetti (2018). In that case, the markup
is only endogenously determined by the number of firms in the economy that in turn is unaffected by the
changes in quality. Therefore, with this specification, changes in quality of goods only have a direct impact
(in the same proportion) on prices and profits.
When the marginal utility is increasing, the average quality level is both negatively determined and has
a negative effect on the other variables in the economy such as labor, investment and output. Following a
productivity shock, as it becomes cheaper to produce consumer goods, the investment in quality by firms
decreases. The negative response of quality produces a positive feedback effect on economy and amplifying
the responses of output, labor and investment.
In contrast, when there is decreasing marginal utility, a positive exogenous shock in the quality of goods
produced leads to a positive response of the consumption, output, labor, markup, firm entry, and prices.
Since a TFP shock has a positive effect on quality, the response is amplified by the positive feedback loop
generated within the model. Therefore, the model produces a larger response of consumption and prices
than in the firm-entry model without endogenous quality.
Since there is no benchmark value to the parameter regulating the marginal utility of quality, I apply the
IRF-matching method to the model, in order to find the value of the parameter most consistent with US data.
I find that the value of parameter that guarantees the impulse-response functions (IRFs) for the model closest
to the ones obtained for the estimated vector autoregression (VAR) is the one implying decreasing marginal
utility. This value is consistent with the hypothesis considered in the main case.
2
In the benchmark specification of the model, It is assumed that quality enters firms’ decisions in the
same form as intermediate inputs or labor – in each period, quality incorporated in consumer goods is equal
to that acquired by firms. This specification is similar to the one used in Jaimovich et al. (2019), where the
authors study the food and drinks service industries.
However, for manufactured goods, the quality of the product does not depend only on the quality of
the inputs. Rather, it depends on the design, technology and innovation which do not disappear with the
manufacturing process, but can become obsolete and require frequent updates. This is translated into the
model by considering the quality as stock, like physical capital. Under the new specification the effect of
quality on other variables is mitigated, as it fluctuates less as a stock. As a result, the model produces IRFs
and second moments closer to the standard firm-entry model.
The remainder of the paper is organized in three sections. In section 2 I present the firm-entry model
and discuss the results obtained under different specifications. Section 3 presents an alternative specification
of quality incorporation at firm level. Section 4 concludes.
2 Model
2.1 Households
Consider a representative household that derives utility fromconsumption at and disutility from supplying
labor lt . Its objective is to maximize expected discounted utility given by
Eo
∞∑t=0
βtU(at, lt ), (1)
where at is the composite consumption index given by
at =
[N∑i=1
(ci,t (xθi,t )
) ε−1ε
] εε−1
, (2)
where ct and xt are the quantity and the quality of each variety consumed, respectively, ε > 1 is the elasticity
of substitution between varieties and θ is the elasticity of quality in the consumption aggregator. The
consumer have the following budget constraint:
vt (Nt + NEt )st+1 + atQt = (πt + vt )Nt st + wt lt, (3)
where v is the value of each firm, π represents the individual firm’s profits, N is the number of firms, NE
stands for the number of newly-created firms, s the share of equity detained by the household and q is the
price of consumer goods adjusted by quality.
The first-order condition for the maximization problem are:
3
−Ul,t
Ua,t=
wt
Qt, (4)
vt = βEt
[Ua,t+1
Ua,t
Qt
Qt+1(vt+1 + πt+1)
], (5)
where 4 is the Frisch labor supply and 5 is the Euler equation for share holdings.
For any given level of consumption ct , the demand of each differentiated variety of goods i = 1, ...,N in
period t must solve the dual problem of minimizing total expendituresN∑i=1
pi,tci,t , subject to the aggregation
constraint in 2. The optimal level of demand ci,t for i = 1, ...,N is given by
ci,t =(Qi,t
Qt
)−εat x
ε(θ−1)−θi,t , (6)
with the nominal quality-adjusted price index, Qt , defined as
Qt =
[N∑i=1
(qi,t
)1−ε di
] 11−ε
, (7)
qi,t =pi,txi,t
. (8)
2.2 Market Structure
In each period, representative household allocate its expenditure E XPt across varieties according to the
demand equation in 6 that can be rewritten as
ci,t =(Qi,t
Qt
)−εE XPt xθ−1
t xε(θ−1)−αi,t , (9)
where E XPt =N∑i=1
pi,tci,t = ctPt = atQt x1−θt . The inverse demand function is then given by
pi,t =c− 1ε
i,t E XPt
N∑i=1(xi,tci,t )
ε−1ε
xα−1ε
t xθ−θ/εi,t . (10)
In each period, the firms seeks to maximize its profits by choosing the quantities of consumer goods to
produce as the strategic variables3:
πi,t (ci,t ) =[pi,t − λi,t
]ci,t − px
t xi,t, (11)
3It is assumed that firm compete over quantities (Cournot) since it leads to a price schedule depending on ε and N . This happensbecause quality (x) is multiplicative in the demand function. Nevertheless, the results for Cournot competition are fairly similar tothe obtained with Bertrand - see Etro and Colciago (2010).
4
where λi,t is themarginal cost and pxt is the price of intermediate quality goods. In ourmodel, the intermediate
quality goods are produced in a separated sector and acquired by firms producing consumer goods to boost
the quality of their products. The demand for quality goods by the producing firms is determined by the
effect of xi,t in demand for their consumer goods ci,t . By substituting equation 10 in 11 and maximizing
profits in order of ci,t we obtain
ε − 1ε
E XPt xθ−1ε
t xθ− θεi,t
©«c− 1ε
i,t
N∑i=1(xi,tci,t )
ε−1ε
−c− ε−1
ε
i,t xi,tN∑i=1(xi,tci,t )
2ε−1ε
ª®®®®¬= λt . (12)
By imposing the symmetry in the Cournot equilibrium we obtain the optimal output of each firm:
ct =ε − 1ε
Nt − 1N2t
E XPt
λtxθ−1t . (13)
Substituting the quantities obtained in the inverse price pt =EXPt
ctNtwe obtain:
pt = µtλt, (14)
where the price markup, µt , depends endogenously on Nt and xt and it is defined as:
µt (ε,Nt, xt ) =ε
ε − 1Nt
Nt − 1x1−θt . (15)
As they choose quantities, firms also choose the level of quality that maximizes their profits. From the
first-order condition we obtain:
pxt = ct xθ−2
t
Ntθ(ε − 1) − ε − θNtε
. (16)
In the symmetric equilibrium, Qt = qtN1
1−εt so that the variety effect is given by
qt = N1ε−1t . (17)
2.3 Firms
In this model it is assumed that the production of each variety of consumer goods only requires labor
input lci,t and is given by
ci,t = pt zt lci,t, (18)
where zt is the aggregate technology, which follows a first-order autoregressive process:
ln(zt ) = ρz ln(zt−1) + uzt , (19)
5
where uzt ∼ N(0, σz) is the exogenous innovation in technology. This gives us the marginal cost λt = wt
zt.
The profits of each firm are given by
πt = (1 −1µt)
ctNt. (20)
As in most of firm-entry models, the number of firms is governed by the law of motion
Nt+1 = (1 − δ)(Nt + NEt ), (21)
where the δ ∈ [1,0] is the exit rate of firms. The creation of new firms is given by
NEt =
zt letφe
, (22)
where let is the labor allocated to firm creation and where φe is the fixed cost of entering the market. Firms
will enter the market until the marginal cost of creating a new firm equals the value of the firm. Therefore,
the firm-entry condition is given by
vt = φewt
zt(23)
with wt
Atdefined as the marginal cost of creating new firms.
The market in quality sector operates under perfect competition, meaning that the price paid by firms in
the consumer goods sector is the same to what would cost if they produced it themselves. The production
function of quality goods is given by
xi,t = it lxi,t, (24)
where lxi,t is the labor input in the production of quality goods and it is the aggregate technology, which
follows a first-order autoregressive process:
ln(ut ) = ρu ln(ut−1) + uit, (25)
where uit ∼ N(0, σi) is the exogenous innovation in technology. The price schedule of quality goods is given
by
pxt =
wt
it. (26)
The model is closed by imposing the labor market clearing condition:
lt = lct + let + lxt . (27)
6
2.4 Calibration and results
For this model, I use the following utility functional form
U(at, lt ) =a1−σt − 11 − σ
− ψl1+χt
1 + χ,
where χ and σ are equal to 1, and the parameter ν is positive and calibrated so, in steady-state, the labor
supply is equal to 1. Since my model is build over the framework of Bilbiie et al. (2012), I follow their
calibration. The discount factor β is set to 0.99, while the exit rate of firms, δ is set to 0.0253. In our
calibration, the elasticity of substitution between varieties is higher than in Bilbiie et al. (2012) and equal to
ε = 5.3. The fixed cost of entry φE is equal to 1. The persistence parameters of productivity and preference
shocks are set to 0.95. The model is solved by first-order perturbation method.
Figure 1: Impulse-response functions to a one percent productivity shock in the firm-entry model with θ = 0.75, 1and 1.5
0 5 10 15 200
2
4Real Output
0 5 10 15 200
1
2 Real Consumption
0 5 10 15 200
2
4
Real Investment
0 5 10 15 200.0
0.2
0.4
Labor
0 5 10 15 200.0
0.5
1.0Wage Rate
0 5 10 15 200.0
0.2
0.4
Number of Firms
0 5 10 15 20
−0.2
0.0
0.2
Price Mar up
0 5 10 15 20−0.5
0.0
0.5
1.0
Price Level
0 5 10 15 200.0
0.2
0.4
0.6
Aggregate Profits
0 5 10 15 20−0.5
0.0
0.5
1.0Quality
0 5 10 15 200
1
2Quality Cost
0 5 10 15 200.00
0.05
0.10
Quality-Adjusted Price
θ=0.75 θ=1 θ=1.5
7
In our model, as in Bilbiie et al. (2012), consumption, output, investment and the wage rate are measured
in nominal terms. To obtain these variables in real terms, one has simply to divide them by pt . In Bilbiie
et al. (2012), real consumption is given by ct/pt , real wage by wt/pt and real investment, since there is no
physical capital, is equal to the total value of new firms created and thus given by netvt/pt . Here, I have to
go further than Bilbiie et al. (2012) and I have thus to add the impact of quality in the real output which is
given by yt = ct xt/pt + netvt/pt .
Figure 1 displays the IRFs to productivity a one percent shock for three different scenarios of endogenous
quality. First we have the scenario where the elasticity of quality is lower than one (θ = 0.75), i.e. quality
has decreasing marginal utility. In the second scenario, quality exhibits constant marginal utility (θ = 1).
Finally, in the third, the elasticity is higher than one (θ = 1.5), i.e. increasing marginal utility over quality.
For the main macro variables such as the output, consumption, investment (measure by netvt/pt ), labor
and wage rate, the IRFs from the model are similar, regardless of the value of θ one chooses. On the other
hand, the variables related to prices, quality and competition behave differently across the parameter values.
When we consider θ = 1, the price markup is only determined by the number of firms. As new firms
enter the market, the markup decreases and the variety effect, measured by the relative price, increases. The
consumer substitutes quality (x) for quantity (c), which is now relatively cheaper. As a result, the aggregate
profits have an initial positive response, as firms spend less in quality goods. Since the price level has a more
positive evolution than quality, the adjusted price, measured by p/x, increases.
For θ > 1, the decrease in quality as a result of the increase in consumption is more pronounced.
Therefore, the price markup displays an initial positive response due to the decrease in quality offsets the
negative impact of firm entry. The profits are higher since firms spend even less in quality goods and the
number of firms increases more as the value of firms is higher due to higher profits.
In contrast, when we consider θ < 1, the model produces a comovement between consumption and
quality. Due to the positive effect of quality, the markup responds less negatively than in the firm-entry-only
case.
Nevertheless, the most important result is the two distinct responses of the price levels - unadjusted and
quality-adjusted. As the firms react to the TFP shock by increasing the quality incorporated in their products,
the (unadjusted) price level increases with it. In fact, this effect accounts for almost the entire variation in
price level as shown by small response of the quality-adjusted price level (0.05% at its peak compared to 1%
peak in raw price level).
Alternatively, we can consider a TFP shock in quality goods (Figure 2).
8
Figure 2: Impulse-response functions to a one percent quality shock in the firm-entry model with θ = 0.75, 1 and 1.5
0 5 10 15 20
0
1
2Real Output
0 5 10 15 200.0
0.5
1.0
1.5
Rea Consumption
0 5 10 15 20
0
2
Rea Investment
0 5 10 15 20−0.4
−0.2
0.0
0.2Labor
0 5 10 15 20
0.00
0.25
0.50
Wage Rate
0 5 10 15 20
−0.2
0.0
Number of Firms
0 5 10 15 20
−0.50
−0.25
0.00
Price Markup
0 5 10 15 200.0
0.5
1.0
Price Leve
0 5 10 15 200.0
0.5
1.0
1.5
Aggregate Profits
0 5 10 15 200.0
0.5
1.0
Qua ity
0 5 10 15 20
0.0
0.5
1.0Qua ity Cost
0 5 10 15 20
−0.05
0.00
Qua ity-Adjusted Price
θ=0.75 θ=1 θ=1.5
For θ = 1, the response of the variables in consumer goods sector to a quality shock is null. Investment,
labor, firm entry, wage rate, and price markup remain constant as the θ = 1 cancels the transmission
mechanism to this part of the economy. Real consumption, profits, and price level increase in direct
proportion to the increment in quality. As a result, the quality-adjusted price remains unchanged.
On other hand, for θ > 1, the increase in quality has a recessionary effect on the economy, leading to a
decrease in firm creation and, by definition, in investment. Due to a reduction in firm creation, the aggregate
demand for labor also decreases. The increase in real wage rate is determined by the joint effect of the
decrease in the markup and the increase in labor productivity in the quality sector.
As it can be seen in Figures 1 and 2, the model calibrated with decreasing marginal utility in quality
consumption produces the IRFs most consistent with empirical evidence. In Figure 3, I compare the model
with decreasing marginal utility on quality and the model without endogenous quality.
9
Figure 3: Impulse-response functions to a one percent TFP shock in firm-entry model with and without endogenousquality
0 5 10 15 200
1
2
3
4Output
0 5 10 15 200.0
0.5
1.0
1.5
2.0Consumption
Firm Entry Firm Entry plus Quality Without Quality Adjustment
0 5 10 15 200
2
4
Investment
0 5 10 15 200.0
0.1
0.2
0.3
0.4
0.5Labor
0 5 10 15 200.0
0.2
0.4
0.6
0.8
1.0
Wage Rate
0 5 10 15 200.0
0.1
0.2
0.3
0.4
0.5Firms
0 5 10 15 20
−0.15
−0.10
−0.05
0.00Price Mar up
0 5 10 15 20
0.0
0.5
1.0
Price Level
0 5 10 15 200.0
0.2
0.4
0.6
Aggregate Profits
In comparison with the firm-entry model, the model with endogenous quality is able to produce a larger
and hump-shaped response in consumption, even when one does not adjust real consumption by the increase
in quality (ct/pt ). However, the response of investment is weaker than the one observed in firm-entry-only
model, leading to a lower response of aggregate output.
When the effect quality on price level is removed, the response of the price level is smaller (solid line) and
closer to the one obtained for from firm-entry-only (blue doted). Additionally, the IRF of real consumption,
adjusted by the improvement in quality, is amplified, leading to a greater response of aggregate output. This
is consistent with the findings from Broda and Weinstein (2010), which state that, with a correction of the
quality bias present in the deflators, the variance observed in the data for the real variables would be larger.
The response of investment is very similar in both cases since the pt is not very large in any of the models.
10
2.5 IRF-matching and second moments
In Figure 3 I assumed that the marginal utility from quality goods specified in the consumption aggregator
is decreasing and θ = 0.75. However, up to this point we do not know what is the true value of this
parameter.To accomplish this, we resort to the methodology presented in Hall et al. (2012).
I consider a recursive VAR xt f pt ≡ [TFPt HOURSt GDPt PCEt µt Πt ], where TFPt is total-
factor productivity, HOURSt is the indicator for total working hours in non-farm business, GDPt the real
Gross Domestic Product, PCEt the real personal consumption expenditure, µt is the average price markup
andΠt are the corporate profits4. I use quarterly data for the period 1960:I to 2017:IV. In the VAR estimation
I use four lags5, one constant, one trend, and all variables are in logarithms. Having the impulse-response
functions IRe for the VAR, I denote a vector of parameters Θ = [ρ, θ] and compute the impulse-response
functions IRm(Θ) for the model. The estimated parameter vector Θ is the one that minimizes the distance
between IRe and IRm(Θ) according to the following equation
Θ = argminΘ[IRe − IRm(Θ)]′W[IRe − IRm(Θ)],
where W is the weighting matrix, corresponding to the inverse of the variance-covariance matrix of IRe.
The IRF-matching is runned on the firm-entry model with endogenous quality and I estimate the values
for θ and ρ. From the IRF-matching between the VAR and the firm-entry model, I estimated the value of θ
to be equal 0.869, while ρ is equal to 0.916. This results, allows us to focus onwards on the results obtained
for case where θ < 1.
Figure 4 presents the response of both the estimated VAR and the theoretical calibrated model. We can
observe that the response of real consumption6 from the model matches almost exactly the response from
VAR, while the responses of output and hours match the sign but not the profile. On the other hand, the IRFs
from estimated VAR and calibrated model for markup and profits display the same profile but they are less
negative in the estimated VAR.
To further assess the fitness of the model to the data, I compare the second moments observed in the
US data and the results from the models with and without endogenous quality in Table 1. To allow the
comparability with the results obtained by Bilbiie et al. (2012), I define χ = 1/4, l = 1, ρa = 0.979 and
variance of uat equal to 0.00722. The second moments for variables of consumption, output and investment
are calculated in real terms.4The estimation of TFP and the price markup as well as the data sources used in our calculations are presented in Appendix B.5Since I am working with quarterly data, the rule of thumb in the VAR specification is four lags.6As for the second moments, I assume that real consumption and real output in the data do not take fully into account quality
changes so I only correct them by using the price level pt .
11
Figure 4: Impulse-response functions to a one percent productivity shock for estimated VAR and the calibrated model
As stated previously, to obtain the data-consistent variables in firm-entry models, the real consumption,
investment and output need to be corrected by the price level. Up to this point, I corrected even further, by
adjusting it also by the quality level. However, since statistical authorities do not take fully into the changes
in quality of the products7 and to increase the comparability with second moments for the firm-entry-only
model, the nominal variables are only corrected using the price level pt .
When observing the standard deviation of the models (σ(X)), one notices that, besides real consumption
and real wage, the model with endogenous quality displays a lower standard deviation. In relative terms
(σ(X)/σ(Y )), investment and labor present significantly lower volatility in comparison with the baseline
model. In fact, the standard deviation of labor is moment where the model with quality performs worse in
comparison with data.
7See Broda and Weinstein (2010).
12
Table 1: Second moments of main macroeconomic variables from US data for 1960:I-2017:IV, firm-entry model andendogenous quality model
Data Firm Entry Firm Entry + Quality
σ(X) σ(X)σ(Y) AC r(X,Y ) σ(X) σ(X)
σ(Y) AC r(X,Y ) σ(X) σ(X)σ(Y) AC r(X,Y )
Y 1.46 1.00 0.86 1.00 1.54 1.00 0.69 1.00 1.04 1.00 0.68 1.00C 1.20 0.82 0.87 0.87 0.77 0.50 0.77 0.94 0.99 0.95 0.78 0.99I 6.59 4.51 0.82 0.90 5.76 3.74 0.66 0.97 3.48 3.35 0.21 0.60L 1.81 1.24 0.92 0.86 0.90 0.58 0.66 0.97 0.14 0.13 0.47 0.95W 0.70 0.48 0.92 0.32 0.96 0.62 0.75 0.98 0.99 0.95 0.74 0.99µ 0.74 0.51 0.55 -0.12 0.06 0.04 0.95 -0.16 0.06 0.06 0.87 -0.73Π 7.96 5.45 0.80 0.59 0.74 0.48 0.76 0.96 0.55 0.53 0.20 0.56
As for the other macro variables, the presence of endogenous quality allows the model to match the
second moments closely observed for consumption and improve the results obtained for both the markup
and aggregate profits.
Table A.2 in the appendix presents the second moments for the model with θ equal to 1 and 1.5. As the
value of θ increases, the model produces lower standard deviations. For some variables, such as investment,
labor and profits, the persistence of shocks, measured by the autocorrelation, also decreases. At the same
time, the increase in θ produces a price markup more negatively correlated with the output.
The second moments obtained for the different values of θ suggest that a model with a θ < 1 produces
results that are more consistent with the data.
3 Quality as a stock
Up to this point, it was assumed that the quality of each variety of consumption goods was equal to the
output of quality sector, meaning that the quality of goods consumed can have significant fluctuation between
periods. This can be plausible for services industries - e.g. food services - where quality depends directly on
the inputs used, but not so much for consumer goods - e.g. gadgets - where most of the quality depends on
technology and design behind the product. In consumer goods, the increase in quality is mostly determined
by innovation, where new improvements add to the pre-existing quality.
Here, we consider that the quality of each variety is a stock that evolves according to the following law
of motion
xi,t+1 = (1 − δx)xi,t + invi,t, (28)
where invi,t is the improvement in x, equal to the output of quality sector, and δx is the depreciation rate of
13
quality. The profits of firms in the consumer goods sector are now given by
πi,t (ci,t ) =[pi,t − λi,t
]ci,t − px
t invi,t, (29)
and the first-order condition for the demand of quality goods is:
pxt − (1 − δx)px
t+1 = ct xθ−2t
Ntθ(ε − 1) − ε − θNtε
. (30)
As there are no reference values for δx , I consider a δx = 0.1, meaning that a given variety becomes
obsolete within 2.5 years. This value of depreciation, that is higher than δ = 0.253 considered for the exit
rate of the firms, is low enough to guarantee dynamics different from the main model, while high enough to
avoid the low volatility generated by the stock of quality goods. Figure 5 presents the IRFs from the model
for different values of θ.
Figure 5: Impulse-response functions to a one percent TFP shock for quality-as-stock model
0 5 10 15 200.0
0.5
1.0
Real Output
0 5 10 15 200.0
0.5
1.0
Real Consumption
0 5 10 15 200
1
2
3Real Investment
0 5 10 15 200.0
0.1
0.2
0.3
Labor
0 5 10 15 200.0
0.5
1.0
Wage Rate
0 5 10 15 200.0
0.2
0.4Number of Firms
0 5 10 15 20
−0.75
−0.50
−0.25
0.00Price Mar up
0 5 10 15 200.0
0.1
0.2
Price Level
0 5 10 15 20
−1.0
−0.5
0.0
0.5Aggregate Profits
0 5 10 15 20
0.00
0.05
0.10
0.15Quality
0 5 10 15 200.0
0.5
1.0
Quality Cost
0 5 10 15 200.00
0.05
Quality-Adjusted Price
θ=0.75 θ=1 θ=1.5
The impulse responses obtained from the model with stock of quality are similar to the ones from our
main model, with the exception for the impulse responses for values of θ higher than one. For these values,
14
the model generates IRFs of investment, labor and firm entry below the ones observed in our main model. At
the same time, the aggregate profits now exhibit a negative response to TFP shocks because quality responds
positively leading to lower markup and higher costs. As the markup is lower for a longer period, the real
wage response is also more persistent.
Figure 6: Impulse-response functions to a productivity shock for estimated VAR and the calibrated model with qualityas a stock
For θ < 1, the only difference is that the response of aggregate profits, which is now positive, determined
by a lower cost imposed by the increase in quality. With the new quality specification, the model produces
impulse responses that match closely the ones observed for the model with only firm entry - see Figure
C.8. Since the quality of goods specified as stock exhibits lower volatility through the business cycle, its
effect on other variables is mitigated. As a result, the model with low δx generates IRFs closer to the ones
for firm-entry-only, while with high δx the IRFs are closer to the ones in benchmark model of endogenous
quality.
As in the previous section, one can estimate the "true" value of the parameter θ in the model with quality
15
as a stock using the IRF-matching method. In this case, the value that minimizes the distance of IRFs of
the model to the ones from the VAR is 0.646 (and ρ = 0.92). The lower value of θ is explained by the
relatively lower effect of quality as a stock, which requires values of θ further away from 1. Figure 6 presents
the IRFs for the estimated VAR and the calibrated model. In comparison with the results obtained for the
benchmark model, presented in Figure 4, the calibrated quality-as-stock model generates IRF of labor closer
to the ones obtained for the estimated VAR. However, this result is obtained at the cost of a less accurate IRF
of consumption and profits, where the benchmark model performs significantly better. Likewise, second
moments of investment and labor obtained for the model with θ = 0.75 are also more in line with the
ones generate by US data, while producing variables of consumption and profits less correlated with output.
(Table C.4).
4 Conclusion
In recent years, a considerable amount of literature on dynamics of product creation and destruction, as
well as its effects on prices, was produced. Simultaneously, the literature on general equilibrium models
addressed the dynamics of product creation and destruction through the introduction of endogenous firm
entry. In these models prices and markups dynamics through the business cycle are fully determined through
the number of varieties (i.e. firms) in the economy. However, as found in Bils (2009) and Broda and
Weinstein (2010), quality changes account for a significant part of price dynamics.
To address this gap in general equilibrium models literature, a mechanism of endogenous quality in
consumption was introduced in a standard firm-entry model. With endogenous quality, the model is able to
replicate the response of product quality and prices observed in data8, while maintaining all the desirable
properties of the firm-entry models.
The way in which quality of each variety is introduced in aggregate consumption allows for its marginal
utility to be defined as either decreasing, constant or increasing. As such, the value assumed for the parameter
regulating the marginal utility generated by quality determines the effect of quality on the markup, prices,
profits, and entry decisions of firms. When the marginal utility obtained from quality of goods consumed is
constant (θ = 1), the transmission of quality to other variables is shut down and changes in quality only have
an effect on the unadjusted price level (higher quality, higher prices), profits (higher prices, higher profits)
and composite consumption (due to higher quality of goods consumed). For increasing marginal utility,
positive changes in quality have a negative impact on the economy as firms trade away the quantity produced
for the increased quality in their products. The reduction in the quantities of goods consumed leads to a
reduction in labor demand, investment, and the markup.
However, when quality is considered to provide decreasing marginal utility (θ < 1)9, the response of
8See Bils (2009) and Broda and Weinstein (2010), as stated above.9This is the case where the model matches best with data – see subsection 2.5.
16
quality to a TFP shock is positive, leading to a feedback loop that is only partly offset by the response of the
average price markup. When compared with the canonical firm-entry model, the introduction of endogenous
quality amplifies the IRF for consumption and output, and produces a less negative response for the price
markup due to the positive effect of quality. With the inclusion of endogenous quality, the firm entry model
improves its second moments for real consumption and aggregate profits.
Moreover, firms in consumer goods markets respond by increasing the quality incorporated in their
goods and, with it, the prices charged to consumers. With endogenous quality, the firm-entry model has
two different sources of price changes – quality and variety. In fact, this effect of quality accounts most of
variation in price level after a TFP shock, which is consistent with the findings in Bils (2009).
Finally, in contrast with the benchmark model, where quality consumed by households is equal to the
amount defined by firms every period, I considered an alternative specification where the quality goods can
be accumulated by firms through a law of motion similar to the one of capital accumulation10.
While the definition of quality as a flow is appropriate when one considers the services industries, where
the quality crucially depends on the inputs used in each period, the quality-as-stock approach is closer to
what is observed in the production of goods, where the quality of each product depends on the investment
from firms in R&D and equipment. This type of investment does not disappear with the production of the
goods but rather become obsolete over time.
With quality defined as a stock, its effect on the economy is weakened since the volatility of stocks is
smaller. Nevertheless, the model holds the same properties and still outperforms the standard firm-entry
model.
References
Afonso, A. and Costa, L. F. (2013). Market power and fiscal policy in OECD countries. Applied Economics, 45(32):4545–4555.Bilbiie, F. O., Ghironi, F., and Melitz, M. J. (2012). Endogenous Entry, Product Variety, and Business Cycles. Journal of Political
Economy, 120(2):304–345.Bils, M. (2009). Do Higher Prices for New Goods Reflect Quality Growth or Inflation?*. The Quarterly Journal of Economics,
124(2):637–675.Broda, C. and Weinstein, D. E. (2010). Product Creation and Destruction: Evidence and Price Implications. American Economic
Review, 100(3):691–723.Colciago, A. and Etro, F. (2010). Real business cycles with Cournot competition and endogenous entry. Journal of Macroeconomics,
32(4):1101 – 1117.Etro, F. and Colciago, A. (2010). Endogenous Market Structures and the Business Cycle. The Economic Journal, 120(549):1201–
1233.Hall, A. R., Inoue, A., Nason, J. M., and Rossi, B. (2012). Information criteria for impulse response function matching estimation
of DSGE models. Journal of Econometrics, 170(2):499 – 518. Thirtieth Anniversary of Generalized Method of Moments.
10See section 3.
17
Hamano, M. and Zanetti, F. (2018). On Quality and Variety Bias in Aggregate Prices. Journal of Money, Credit and Banking,50(6):1343–1363.
Jaimovich, N. and Floetotto, M. (2008). Firm dynamics, markup variations, and the business cycle. Journal of Monetary Economics,55(7):1238 – 1252.
Jaimovich, N., Rebelo, S., and Wong, A. (2019). Trading down and the business cycle. Journal of Monetary Economics, 102:96 –121. Carnegie-Rochester-NYUConferenceSeries on Public Policy“AConference Honoring the Contributions ofCharles Plosserto Economics”Held at the University of RochesterSimon Business SchoolApril 20-21, 2018.
Schmitt-Grohé, S. and Uribe, M. (2012). On quality bias and inflation targets. Journal of Monetary Economics, 59(4):393 – 400.
18
A Main Model
Figure A.7: Impulse-response functions to three types of shocks for the main model
0 5 10 15 200
2
4
6Real Output
0 5 10 15 200
1
2
3
Real Consumpt on
0 5 10 15 200.0
2.5
5.0
7.5
Real Investment
0 5 10 15 200.0
0.2
0.4
Labor
0 5 10 15 20
0.0
0.5
1.0Wage Rate
0 5 10 15 200.0
0.2
Number of F rms
0 5 10 15 20.0.1
0.0
0.1
0.2Pr ce Markup
0 5 10 15 20
0
1
2
Pr ce Level
0 5 10 15 200
1
2
Aggregate Prof ts
0 5 10 15 20
0
1
2
Qual t−
0 5 10 15 20
0
1
2
Qual t− Cost
0 5 10 15 200.000
0.025
0.050
0.075
Qual t−-Adjusted Price
Productivity Shock Quality Shock Aggregate Shock
19
Table A.2: Second moments of main macroeconomic variables from US data for 1960:I-2017:IV, model with θ = 1and model with θ = 1.5
Data θ = 1 θ = 1.5
σ(X) σ(X)σ(Y) AC r(X,Y ) σ(X) σ(X)
σ(Y) AC r(X,Y ) σ(X) σ(X)σ(Y) AC r(X,Y )
Y 1.46 1.00 0.86 1.00 1.02 1.00 0.69 1.00 1.01 1.00 0.73 1.00
C 1.20 0.82 0.87 0.87 0.99 0.97 0.77 0.99 1.01 1.00 0.77 1.00
I 6.59 4.51 0.82 0.90 2.96 2.90 0.22 0.61 2.10 2.08 0.10 0.52
L 1.81 1.24 0.92 0.86 0.11 0.11 0.33 0.83 0.05 0.05 0.21 0.75
W 0.70 0.48 0.92 0.32 1.01 0.99 0.76 0.99 1.03 1.02 0.78 1.00
µ 0.74 0.51 0.55 -0.12 0.10 0.10 0.84 -0.65 0.14 0.14 0.77 -0.68
Π 7.96 5.45 0.80 0.59 0.70 0.68 0.23 0.41 0.87 0.86 0.14 0.20
B US Data and Markup estimation
As stated in subsection 2.5, I follow Afonso and Costa (2013) in our average markup’s estimation. In
their paper, the short-run markup is a function of labor share and defined as
µt =1 − αt
st
11 − φt
, (B.31)
where st is the labor share, αt is the long-run capital share and φt is the measure of increasing returns
φt =µ∗ − 1µ∗
K∗αtt L∗1−αt
t
Kαtt L1−αt
t
, (B.32)
where µ∗ is steady-state average markup and K∗t and L∗t are the steady-state level of capital and labor input,
respectively. Substituting A.27 into markup equation we obtain
µt =1 − αt
st
µ∗
µ∗ − (µ∗ − 1)xt, (B.33)
where xt =HP(K
αtt L
1−αtt )
Kαtt L
1−αtt
. Both αt and the long-run values of output are obtained through the Hodrick-
Prescott filter. The steady-state markups is same as in Afonso and Costa (2013) and is equal to 1.203.
The TFP series used in the VAR were estimated through the following equation
∆TFPt = ∆(Yht Lt ) − αtKt − (1 − αt )Lt, (B.34)
where Yht Lt is the real output of Nonfarm Business Sector. Table B.3 presents the data sources for the series
used in our estimations.
20
Table B.3: Data sources 1960:I-2017:IV
Variable Series Code Source
Y Real Gross Domestic Product GDPC1 FRED
C Real Personal Consumption Expenditures PCEC96 FRED
L Nonfarm Business Sector: Hours of All Persons HOANBS FRED
Yh Nonfarm Business Sector: Real Output Per Hour of All Persons OPHNFB FRED
K Net Capital Stock OKND AMECO
s Compensation of Employes/Gross Domestic Product COE/GDP FRED
W Nonfarm Business Sector: Real Compensation Per Hour COMPRNFB FRED
π Corporate Profits with IVA and CCAdj CPROFIT FRED
C Quality as stock
Table C.4: Second moments of main macroeconomic variables from US data for 1960:I-2017:IV, for firm-entry modeland firm-entry with quality as stock
Data Firm Entry Firm Entry + Quality
σ(X) σ(X)σ(Y) AC r(X,Y ) σ(X) σ(X)
σ(Y) AC r(X,Y ) σ(X) σ(X)σ(Y) AC r(X,Y )
Y 1.46 1.00 0.86 1.00 1.54 1.00 0.69 1.00 1.29 1.00 0.80 1.00
C 1.20 0.82 0.87 0.87 0.77 0.50 0.77 0.94 0.82 0.64 0.76 0.96
I 6.59 4.51 0.82 0.90 5.76 3.74 0.66 0.97 5.40 4.19 0.85 0.95
L 1.81 1.24 0.92 0.86 0.90 0.58 0.66 0.97 0.74 0.57 0.74 0.90
W 0.70 0.48 0.92 0.32 1.00 0.65 0.76 0.95 0.94 0.73 0.73 0.98
µ 0.74 0.51 0.55 -0.12 0.06 0.04 0.95 -0.16 0.10 0.08 0.95 0.11
Π 7.96 5.45 0.80 0.59 0.74 0.48 0.76 0.96 1.64 1.27 0.50 0.06
21
Figure C.8: Impulse-response functions to a one percent TFP shock for firm-entry model and quality-as-stock model
0 5 10 15 200.00
0.25
0.50
0.75
1.00
1.25Output
0 5 10 15 200.0
0.2
0.4
0.6
0.8
Consumption
Firm Entry Firm Entry plus Quality Without Quality Ad ustment
0 5 10 15 200
1
2
3
Investment
0 5 10 15 200.0
0.1
0.2
0.3
0.4
0.5Labor
0 5 10 15 200.0
0.2
0.4
0.6
0.8
1.0Wage Rate
0 5 10 15 200.0
0.1
0.2
0.3
0.4
0.5Firms
0 5 10 15 20
−0.20
−0.15
−0.10
−0.05
0.00Price Markup
0 5 10 15 200.00
0.05
0.10
0.15
0.20
Price Level
0 5 10 15 20−0.4
−0.2
0.0
0.2
0.4
Aggregate Profits
22
